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## #1 2017-07-31 08:24:43

alvinero
Member
Registered: 2017-07-31
Posts: 1

### Swapping digits problems

Hello, a friend of mine suggested me this problem:

Find a number n that, when you swap the first and last digits, it becomes 2n. Please, try to find it in decimal system.

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## #2 2017-07-31 08:41:13

zetafunc
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Registered: 2014-05-21
Posts: 2,109
Website

### Re: Swapping digits problems

Hi alvinero,

Welcome to the forum. Any restrictions on the number of digits? For instance, n = 0 works. Two digits can be ruled out by letting n = 10a + b (which has no solutions as per your constraints), and three digits can also be ruled out the same way via modulo arithmetic. If a non-trivial solution exists, it may be large.

EDIT: I have a solution, but it is 21 digits long. I don't know if this is the smallest such solution (and, if this was intended to be a quick brain teaser, it seems unlikely to be). I'll post up a rough solution tomorrow.

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## #3 2017-08-03 03:50:38

Nehushtan
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Registered: 2013-03-09
Posts: 905
Website

### Re: Swapping digits problems

Apparently the smallest number has 18 digits.

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## #4 2017-08-04 00:56:53

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,109
Website

### Re: Swapping digits problems

Thanks for the solution, it is an interesting problem.

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